OTC 5L 2s - Revision history

Lériendil: Text replacement - "Category:Tempered_scales↵Category:Pages with mostly numerical content" to "Category:Tempered scales Category:Pages with mostly numerical content"

2025-06-24T03:13:12Z

Text replacement - "Category:Tempered_scales↵Category:Pages with mostly numerical content" to "Category:Tempered scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 03:13, 24 June 2025
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	<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>		<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>
	[[Category:7-tone scales]]		[[Category:7-tone scales]]
	[[Category:~~Tempered_scales~~]]		[[Category:Tempered scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]

Lériendil: Text replacement - "Category:Tempered scales↵Category:Pages with mostly numerical content" to "Category:Tempered_scales Category:Pages with mostly numerical content"

2025-06-24T02:40:35Z

Text replacement - "Category:Tempered scales↵Category:Pages with mostly numerical content" to "Category:Tempered_scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 02:40, 24 June 2025
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	<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>		<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>
	[[Category:7-tone scales]]		[[Category:7-tone scales]]
	[[Category:~~Tempered scales~~]]		[[Category:Tempered_scales]]
	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]

Lériendil: Text replacement - "Category:Tempered scales" to "Category:Tempered scales Category:Pages with mostly numerical content"

2025-06-24T02:35:00Z

Text replacement - "Category:Tempered scales" to "Category:Tempered scales Category:Pages with mostly numerical content"

← Older revision		Revision as of 02:35, 24 June 2025
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	[[Category:7-tone scales]]		[[Category:7-tone scales]]
	[[Category:Tempered scales]]		[[Category:Tempered scales]]
			[[Category:Pages with mostly numerical content]]
	[[Category:MODMOS]]		[[Category:MODMOS]]
	[[Category:Omnitetrachordal]]		[[Category:Omnitetrachordal]]

BudjarnLambeth: Categorised this uncategorised page

2023-05-02T04:36:19Z

Categorised this uncategorised page

← Older revision		Revision as of 04:36, 2 May 2023
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	===References===		===References===
	<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>		<ul><li>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685 3685] and [http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987 10987].</li></ul>
			[[Category:7-tone scales]]
			[[Category:Tempered scales]]
			[[Category:MODMOS]]
			[[Category:Omnitetrachordal]]
			[[Category:Meantone]]
			[[Category:Pythagorean]]
			[[Category:Superpyth]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>spt3125: Imported revision 590306118 - Original comment:

2016-08-28T20:20:58Z

**Imported revision 590306118 - Original comment: **

← Older revision		Revision as of 20:20, 28 August 2016
Line 1:		Line 1:
	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:spt3125\|spt3125]] and made on <tt>2016-08-28 20:15:21 UTC</tt>.<br>		: This revision was by author [[User:spt3125\|spt3125]] and made on <tt>2016-08-28 20:20:58 UTC</tt>.<br>
	: The original revision id was <tt>~~590305916~~</tt>.<br>		: The original revision id was <tt>590306118</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
	<h4>Original Wikitext content:</h4>		<h4>Original Wikitext content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[5L 2s\|5L+2s]] / 7 tones (3+1+3)		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Omnitetrachordal MOS scale
	~~Classic~~ diatonic ~~MOS~~ scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1\|(1)]]		[[5L 2s\|5L+2s]]
			7 tones (3+1+3)

			The classic diatonic scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1\|(1)]]

	[[Gallery of omnitetrachordal scales#perfect\|P]] = 2.2600167527 (L=9/8, s=[[256_243\|256/243]])		[[Gallery of omnitetrachordal scales#perfect\|P]] = 2.2600167527 (L=9/8, s=[[256_243\|256/243]])
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	[[image:07_05_02_LsL_L_Ls.png]]		[[image:07_05_02_LsL_L_Ls.png]]

			===See also===
			* [[Omnitetrachordality]]
			* [[Gallery of omnitetrachordal scales]]

			===References===
	* [[#ref1]](1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685\|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987\|10987]].</pre></div>		* [[#ref1]](1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685\|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987\|10987]].</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>OTC 5L 2s</title></head><body><a class="wiki_link" href="/5L%202s">5L+2s</a> / 7 tones (3+1+3)<br />		<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>OTC 5L 2s</title></head><body>Omnitetrachordal MOS scale<br />
	~~Classic~~ diatonic ~~MOS~~ scale (<a class="wiki_link" href="/meantone">meantone</a>, Pythagorean, <a class="wiki_link" href="/superpyth">superpyth</a>). <!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1\|(1)]] --><a class="wiki_link" href="/OTC%205L%202s#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:01 --><br />		<a class="wiki_link" href="/5L%202s">5L+2s</a><br />
			7 tones (3+1+3)<br />
			<br />
			The classic diatonic scale (<a class="wiki_link" href="/meantone">meantone</a>, Pythagorean, <a class="wiki_link" href="/superpyth">superpyth</a>). <!-- ws:start:WikiTextVariableComponentRule:01:[[{$page}#ref1\|(1)]] --><a class="wiki_link" href="/OTC%205L%202s#ref1">(1)</a><!-- ws:end:WikiTextVariableComponentRule:01 --><br />
	<br />		<br />
	<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 2.2600167527 (L=9/8, s=<a class="wiki_link" href="/256_243">256/243</a>)<br />		<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 2.2600167527 (L=9/8, s=<a class="wiki_link" href="/256_243">256/243</a>)<br />
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	<br />		<br />
	<!-- ws:start:WikiTextLocalImageRule:~~179~~:&lt;img src=&quot;/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png" alt="07_05_02_LsL_L_Ls.png" title="07_05_02_LsL_L_Ls.png" /><!-- ws:end:WikiTextLocalImageRule:~~179~~ --><br />		<!-- ws:start:WikiTextLocalImageRule:189:&lt;img src=&quot;/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png" alt="07_05_02_LsL_L_Ls.png" title="07_05_02_LsL_L_Ls.png" /><!-- ws:end:WikiTextLocalImageRule:189 --><br />
	<br />		<br />
	<ul><li><!-- ws:start:WikiTextAnchorRule:2:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@ref1&quot; title=&quot;Anchor: ref1&quot;/&gt; --><a name="ref1"></a><!-- ws:end:WikiTextAnchorRule:2 -->(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html></pre></div>		<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc0"><a name="x--See also"></a><!-- ws:end:WikiTextHeadingRule:2 -->See also</h3>
			<ul><li><a class="wiki_link" href="/Omnitetrachordality">Omnitetrachordality</a></li><li><a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales">Gallery of omnitetrachordal scales</a></li></ul><br />
			<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc1"><a name="x--References"></a><!-- ws:end:WikiTextHeadingRule:4 -->References</h3>
			<ul><li><!-- ws:start:WikiTextAnchorRule:6:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@ref1&quot; title=&quot;Anchor: ref1&quot;/&gt; --><a name="ref1"></a><!-- ws:end:WikiTextAnchorRule:6 -->(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html></pre></div>

Wikispaces>spt3125: Imported revision 590305916 - Original comment:

2016-08-28T20:15:21Z

**Imported revision 590305916 - Original comment: **

New page

<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference: 
: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2016-08-28 20:15:21 UTC</tt>. 
: The original revision id was <tt>590305916</tt>. 
: The revision comment was: <tt></tt> 
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it. 
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[5L 2s|5L+2s]] / 7 tones (3+1+3)
Classic diatonic MOS scale ([[meantone]], Pythagorean, [[superpyth]]). [[{$page}#ref1|(1)]]

[[Gallery of omnitetrachordal scales#perfect|P]] = 2.2600167527 (L=9/8, s=[[256_243|256/243]])

L = 171.43 to 240.00 cents (203.91 cents @ P)
s = 0.00 to 171.43 cents (90.22 cents @ P)

9/8 = L (171.43 to 240.00 cents)
4/3 = 2L+s (480.00 to 514.29 cents)
generator = 3L+s (685.71 to 720.00 cents)

notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc.

symmetric mode: LsLLLsL

all modes:
|| || {{ LLs L LLs }} || || Ionian ||= 5|1 ||
|| || {{ LsL L LsL }} || || Dorian ||= 3|3 ||
|| || {{ sLL L sLL }} || || Phrygian ||= 1|5 ||
|| {{ L LLs LLs }} || || || Lydian ||= 6|0 ||
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||= 4|2 ||
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||= 2|4 ||
|| || || {{ sLL sLL L }} || Locrian ||= 0|6 ||

all modes in [[Modal UDP Notation|UDP]] order:
|| {{ L LLs LLs }} || || || Lydian ||= 6|0 ||
|| || {{ LLs L LLs }} || || Ionian ||= 5|1 ||
|| {{ L LsL LsL }} || || {{ LLs LLs L }} || Mixolydian ||= 4|2 ||
|| || {{ LsL L LsL }} || || Dorian ||= 3|3 ||
|| {{ L sLL sLL }} || || {{ LsL LsL L }} || Aeolian ||= 2|4 ||
|| || {{ sLL L sLL }} || || Phrygian ||= 1|5 ||
|| || || {{ sLL sLL L }} || Locrian ||= 0|6 ||

[[image:07_05_02_LsL_L_Ls.png]]

* [[#ref1]](1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages [[http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685|3685]] and [[http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987|10987]].</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>OTC 5L 2s</title></head><body><a class="wiki_link" href="/5L%202s">5L+2s</a> / 7 tones (3+1+3) 
Classic diatonic MOS scale (<a class="wiki_link" href="/meantone">meantone</a>, Pythagorean, <a class="wiki_link" href="/superpyth">superpyth</a>). <a class="wiki_link" href="/OTC%205L%202s#ref1">(1)</a> 
 
<a class="wiki_link" href="/Gallery%20of%20omnitetrachordal%20scales#perfect">P</a> = 2.2600167527 (L=9/8, s=<a class="wiki_link" href="/256_243">256/243</a>) 
 
L = 171.43 to 240.00 cents (203.91 cents @ P) 
s = 0.00 to 171.43 cents (90.22 cents @ P) 
 
9/8 = L (171.43 to 240.00 cents) 
4/3 = 2L+s (480.00 to 514.29 cents) 
generator = 3L+s (685.71 to 720.00 cents) 
 
notable EDOs: 12, 17, 19, 22, 26, 29, 31, etc. 
 
symmetric mode: LsLLLsL 
 
all modes: 

<table class="wiki_table">
<tr>
<td> 
</td>
<td><tt> LLs L LLs </tt> 
</td>
<td> 
</td>
<td>Ionian 
</td>
<td style="text-align: center;"> 5|1 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> LsL L LsL </tt> 
</td>
<td> 
</td>
<td>Dorian 
</td>
<td style="text-align: center;">3|3 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> sLL L sLL </tt> 
</td>
<td> 
</td>
<td>Phrygian 
</td>
<td style="text-align: center;">1|5 
</td>
</tr>
<tr>
<td><tt> L LLs LLs </tt> 
</td>
<td> 
</td>
<td> 
</td>
<td>Lydian 
</td>
<td style="text-align: center;">6|0 
</td>
</tr>
<tr>
<td><tt> L LsL LsL </tt> 
</td>
<td> 
</td>
<td><tt> LLs LLs L </tt> 
</td>
<td>Mixolydian 
</td>
<td style="text-align: center;">4|2 
</td>
</tr>
<tr>
<td><tt> L sLL sLL </tt> 
</td>
<td> 
</td>
<td><tt> LsL LsL L </tt> 
</td>
<td>Aeolian 
</td>
<td style="text-align: center;">2|4 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> sLL sLL L </tt> 
</td>
<td>Locrian 
</td>
<td style="text-align: center;">0|6 
</td>
</tr>
</table>

 
all modes in <a class="wiki_link" href="/Modal%20UDP%20Notation">UDP</a> order: 

<table class="wiki_table">
<tr>
<td><tt> L LLs LLs </tt> 
</td>
<td> 
</td>
<td> 
</td>
<td>Lydian 
</td>
<td style="text-align: center;"> 6|0 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> LLs L LLs </tt> 
</td>
<td> 
</td>
<td>Ionian 
</td>
<td style="text-align: center;">5|1 
</td>
</tr>
<tr>
<td><tt> L LsL LsL </tt> 
</td>
<td> 
</td>
<td><tt> LLs LLs L </tt> 
</td>
<td>Mixolydian 
</td>
<td style="text-align: center;">4|2 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> LsL L LsL </tt> 
</td>
<td> 
</td>
<td>Dorian 
</td>
<td style="text-align: center;">3|3 
</td>
</tr>
<tr>
<td><tt> L sLL sLL </tt> 
</td>
<td> 
</td>
<td><tt> LsL LsL L </tt> 
</td>
<td>Aeolian 
</td>
<td style="text-align: center;">2|4 
</td>
</tr>
<tr>
<td> 
</td>
<td><tt> sLL L sLL </tt> 
</td>
<td> 
</td>
<td>Phrygian 
</td>
<td style="text-align: center;">1|5 
</td>
</tr>
<tr>
<td> 
</td>
<td> 
</td>
<td><tt> sLL sLL L </tt> 
</td>
<td>Locrian 
</td>
<td style="text-align: center;">0|6 
</td>
</tr>
</table>

 
<img src="/file/view/07_05_02_LsL_L_Ls.png/589273784/07_05_02_LsL_L_Ls.png" alt="07_05_02_LsL_L_Ls.png" title="07_05_02_LsL_L_Ls.png" /> 
 
<ul><li><a name="ref1"></a>(1) Noted as omnitetrachordal by Paul Erlich no later than 2002. See tuning-math list messages <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s___4/msg_3675-3699.html#3685" rel="nofollow">3685</a> and <a class="wiki_link_ext" href="http://robertinventor.com/tuning-math/s__11/msg_10975-10999.html#10987" rel="nofollow">10987</a>.</li></ul></body></html></pre></div>